In this work, our goal is to develop an intermediate family of methods that “interpolate” MCMC and VI, inspired by a simple and intuitive picture (Figure REF ): we propose constructing a stochastic process in the space of variational parameters such that the resulting approximation is a stochastic mixture of variational “component” distributions. This extends sampling by replacing the sampled points with extended components, analogous to kernel density estimation but in the space of inferred rather than observed variables. It extends VI by replacing the single best-fitting variational distribution with a stochastic mixture of more localized components. This is qualitatively distinct from previous variational methods that use stochastic optimization: rather than stochastically optimizing a single variational approximation [1]}, [2]}, we use stochasticity to construct a random mixture of variational components that achieves lower asymptotic bias than any one component could. We will further show below how classic sampling and classic variational inference emerge as special cases of a single optimization problem.
